Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (1): 142-148.

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Existence of Positive Radial Solution to a Class of Kirchhoff type Equation in ${\mathbb R}$$N$

Yihua Deng()   

  1. College of Mathematics and Statistics, Hengyang Normal University, Hunan Hengyang 421002
  • Received:2019-10-16 Online:2021-02-26 Published:2021-01-29
  • Supported by:
    the NSF of Hunan Province(14JJ2120);the Double Top Application Characteristic Discipline of Hunan Province(湘教通[2018]469);the Fund for Intelligent Information Processing and Application Key Laboratory of Hunan Province(2016TP1020)

Abstract:

In this paper, we discuss a class of Kirchhoff type equation whose energy function may not be of $C^1$ class. This equation is closely related to plasma physics and theories for propagation of laser beams. Using a change of variables, we get a new equivalent equation whose energy function is of $C^1$ class. Using a suitable Banach space and variational method, we prove that there is a positive radial solution to the given equation under proper conditions.

Key words: Kirchhoff type equation, Positive radial solution, Variational method, Banach space

CLC Number: 

  • O175.2
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